Efficient approximate planning in continuous space Markovian Decision Problems

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Continuous Doubly Constrained Batch Reinforcement Learning (2021, background): “TCDC is a L∞ contraction under standard conditions that suffice for the ordinary Bellman operator to be contractive [3, 6, 8, 56].”
Algorithms for Reinforcement Learning (2010, background): “…worst-case can scale exponentially with the dimensionality of the state space (Chow and Tsitsiklis, 1989), while online planning (i.e., planning for the “current state”) can break the curse of dimensionality by amortizing the planning effort over multiple time steps (Rust, 1996; Szepesvári, 2001).”
Finite-Time Bounds for Fitted Value Iteration (2008, methodology): “17 of Szepesvári (2001) yields that for all state x ∈ X , |V πK α,λ(x)− V πK α (x)| ≤ 2Vmaxλ 1− γ .”
Finite time bounds for sampling based fitted value iteration (2005, background): “When the MDP’s transition kernel possesses a bounded density, a case that is often considered in previous theoretical works (Chow and Tsitsiklis, 1989, 1991; Rust, 1996b; Szepesvári, 2000), then the t-step concentrability factors stay bounded and hence their discounted-average obeys the same bound.”